A NEW SCALARIZATION FUNCTION AND WELL-POSEDNESS OF VECTOR OPTIMIZATION PROBLEM

In this paper, a new scalarization function which is Gerstewitz type and nonlinear is introduced. This function can be used to scalarize not only solid but also non,-solid optimization problems. A few properties of this newly defined function are established. Two types of well-posedness are considered for a vector optimization problem (V, f) in terms of its weak eift-cient solutions. Using the above function, a scalar problem SOP (V, f) cor-responding to (V, f) is considered. Few characterizations of weak minimal solutions of (V, f) in terms of solutions of SOP (V, f) are obtained. Equiv-alence of well-posedness of (V, f) with that of SOP (V, f) is established. At the end, a characterization of well-posedness of (V, f) with respect to level set is given.